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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="waybel_4.html#V4">auxiliary(iv)</a> <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">D</font> being   <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>  st <font color="Maroon">C</font> <a href="lattice7.html#R1">c=</a> <font color="Olive">D</font> holds <br/><font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Olive">D</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel35.html#D4" target="_self">WAYBEL35:def 4</a><br/>

<b>assume </b><a NAME="E2:36"/><i><font color="Green">E31</font></i>: 
not  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E3:36"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">C</font> <a href="lattice7.html#R1">c=</a> <font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:36"/>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> is    <a href="waybel35.html#M1" target="_self">strict_chain</a> of <font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:36"/><b>then </b>
<font color="Maroon">C</font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:36"/><b>then </b>
not  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:36"/>
contradiction
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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